Mathematics and Computer Science

Enrique Treviño’s paper published in American Mathematical Monthly

Professor Enrique Treviño’s paper “The primes that Euclid Forgot” co-authored with Paul Pollack from the University of Georgia was published in the May issue of the American Mathematical Monthly, the most widely read mathematics journal in the world.

Over 2000 years ago, Euclid proved that there are infinitely many prime numbers. Prime numbers are positive integers greater than 1 that cannot be divided by any number other than itself and 1. For example, 2, 3, 5, 7, 11, 13, 17, 19 are the first 8 prime numbers. Every positive integer can be factored into primes, so primes are often called the “atoms of the integers”. Euclid’s proof that there infinitely many primes suggests the construction of many infinite sequences of primes. Mullin in 1963 asked if two of those sequences covered all the primes. In 2012, Booker proved that the second Euclid-Mullin sequence missed infinitely many primes. In the paper just published, Paul Pollack and Enrique Treviño gave a simplified proof of Booker’s result that there are infinitely many primes missing from the second Euclid-Mullin sequence.

Professor Treviño has presented these results as an invited speaker at the Joint Mathematics Meeting in Baltimore in January 2014 and at an invited talk at Oberlin College in March 10, 2014.